1. The Angle Addition Postulate Angle Addition Postulate
For any angle PQR, if A is in the interior of PQR, then mPQA + mAQR = mPQR. 2 1 A R P Q
m1 + m2 = mPQR.
There are two equations that can be derived using Postulate 4.
m1 = mPQR – m2
These equations are true no matter where A is located in the interior of PQR.
m2 = mPQR – m1

2. The Angle Addition Postulate
Find mABC and mCBD if mABD = 120.
mABC + mCBD = mABD
Postulate 4
2x + (5x – 6) = 120
Substitution
7x – 6 = 120
Combine like terms
7x = 126
Add 6 to both sides
x = 18
Divide each side by 7
= 120
2x°
(5x – 6)° B D C A
mABC = 2x
mCBD = 5x – 6
mABC = 2(18)
mCBD = 5(18) – 6
mABC = 36
mCBD = 90 – 6
mCBD = 84

3. Geometry is built on statements called _________.
Postulates
postulates
Geometry is built on statements called _________.
Postulates are statements in geometry that are accepted to be true.
Postulate 5: A line contains at least 2 points
A plane contains at least 3 points not all in one line
Space contains at least 4 points not all in one line Q P A B C

4. Postulate 6: Two points determine a unique ___.
Postulates
Postulate 6: Two points determine a unique ___. Q P
line
There is only one line that contains Points P and Q T l m
Theorem 1-1: If two distinct lines intersect, then their intersection is a ____.
point
Lines l and m intersect at point T
Postulate 7: Three noncollinear points determine a unique _____. A B C
plane
There is only one plane that contains points A, B, and C.

5. Postulates
Points A, B, and C are noncollinear. A
1) Name all of the different lines that can be drawn through these points. C B
2) Name the intersection of
Point C

6. Postulates
1) Name all of the planes that are represented in the figure. B A D C

7. Postulates
1) Name all of the planes that are represented in the figure.
There is only one plane that contains three noncollinear points. B A D C
plane ABC (side)
plane ACD (side)
plane ABD (back side)
plane BCD (bottom)

8. Postulate 8: If two points are in a plane, then the line
Postulates
Postulate 8: If two points are in a plane, then the line
That contains the points is in that plane A B
The line that contains points A and B is in the
plane shown.

9. Postulates
Postulate 9: If two distinct planes intersect, then their intersection is a ___.
line
Plane M and plane N intersect in line DE. M N D E

10. Name the intersection of plane CDG and plane BCD.
Postulates
Name the intersection of plane CDG and plane BCD. H E F G C B A D

11. Name the intersection of plane CDG and plane BCD.
Postulates
Name the intersection of plane CDG and plane BCD.
Name two planes that intersect in
planes ADF and CDF H E F G C B A D